LDA band structures of LDA band structures of transition-metal oxidestransition-metal oxides

Is it really the prototype Mott transition?Is it really the prototype Mott transition?

The metal-insulator transition in VThe metal-insulator transition in V22OO33

and what electronic and what electronic correlations may do to themcorrelations may do to them

Lecture 2.2, XV Training Course in the Physics of Strongly Correlated Systems, IASS Vietri sul Mare

[1] T. Saha-Dasgupta, O.K. Andersen, J. Nuss, A.I. Poteryaev, A. Georges, A.I. Lichtenstein; arXiv: 0907.2841.

[2] A.I. Poteryaev, J.M. Tomczak, S. Biermann, A. Georges, A.I. Lichtenstein, A.N. Rubtsov, T. Saha-Dasgupta, O.K. Andersen; Phys. Rev. B 76, 085127 (2007)

[3] F. Rodolakis, P. Hansmann, J.-P. Rueff, A. Toschi, M.W. Haverkort, G. Sangiovanni, A. Tanaka, T. Saha-Dasgupta, O.K. Andersen, K. Held, M. Sikora, I. Alliot, J.-P. Itié, F. Baudelet, P.Wzietek, P. Metcalf, M. Marsi; Phys. Rev. Lett. 104, 047401 (2010).

[4] S. Lupi, L. Baldassarre, B. Mansart, A. Perucchi, A. Barinov, P. Dudin, E. Papalazarou, F. Rodolakis, J.-P. Rueff, J.-P. Itié, S. Ravy, D. Nicoletti, P. Postorino, G. Sangiovanni, A. Toschi, P. Hansmann, N. ParraghN. Parragh, T. Saha-Dasgupta, O.K. Andersen, K. Held, M. Marsi; (accepted)

Doped Mott Insulators

have rich physical properties

and controlling them is one of

the major challenges for

developing Advanced Materials

High-Temperature Superconductors

Colossal Magneto-Resistance Materials

Intelligent Windows, Field-effect Transistors

Hubbard model LDA+DMFT1/2 filling T=2000K,

U = 3.0 eVU =2.1 eV

T. Saha-Dasgupta and OKA 2002

Wannier orbital Conduction band (LDA)

U/W = 1

U/W = 2

U/W = 2.5

U/W = 3

U/W = 4

Georges and Kotliar 1992:

The single-band Hubbard Model in the d=∞ limit can be mapped exactly onto the Anderson impurity model supplemented by a CPA-like self-consistency condition for the dynamical coupling to the non-interacting medium. Hence, the Kondo-resonance may develop into a quasi-particle peak.

For general hopping, the Georges-Kotliar mapping leads to the dynamical mean-field approximation(DMFT).

A. Georges et al, Rev Mod Phys 1996:

QP

Gap

LHB UHB

W = 1

LDA O.K.

LDA+U O.K.

DMFT needed

DMFT needed

DMFT needed

Mott transition

Electronic-structure calculations for Electronic-structure calculations for materialsmaterials with strong correlations with strong correlations

Current approximations to ab inito Density-Functional Theory (LDA) are insufficient for conduction bands with strong electronic correlations, e.g. they do not account for the Mott metal-insulator transition.

On the other hand, LDA Fermi surfaces are accurate for most

metals, including overdoped high-temperature superconductors.

Presently, we therefore start with the LDA. For the few correlated bands, we then construct localized Wannier orbitals (NMTOs) and a corresponding low-energy Hubbard Hamiltonian: HLDA + Uon-site. This is solved in the dynamical mean-field approximation (DMFT).

V 3dV 3d22

AFI monoclinic

Paramagnetic M and I corundum str

LDA+U: Ezhov, Anisimov, Khomskii, Sawatzky 1999

MM

IIMM

AFI

AFI

II

MM

LDA band structure LDA band structure of Vof V22OO3 3 projected projected

onto various orbital onto various orbital characters:characters:

N=2

N=2

N=2

N=1

Blow up the energy scale Blow up the energy scale and split the panels:and split the panels:

EEFF

EEFF

EEFF

Pick various sub-Pick various sub-bands by bands by generating the generating the corresponding corresponding minimal minimal NNMTO MTO basis set: basis set:

EEFF

For the low-energy For the low-energy Hamiltonian we Hamiltonian we just need the just need the tt2g2g set set

(V(V1-x1-xMMxx))22OO33

VV22OO33

3d (3d (tt2g2g))22

Hund's-rule coupling J=0.7 eV

a1g-egπ crystal-field

splitting = 0.3 eV

Undo Undo hhybridizationybridization

aa1g1g

eeggππ

PMPM

LDA t2g NMTO Wannier Hamiltonian

2.0

LDALDA

PMPM

a1g-e

gπ c

rys

tal-

fie

ld s

pli

ttin

g =

0.3

eV

U-e

nh

an

ce

me

nt

= 1

.85

eV

~ 3J

LDA+DMFT

U = 4.25 eV, J = 0.7 eV

Crystal-field enhanced Crystal-field enhanced and mass-renormalized and mass-renormalized QP bandsQP bands

PM

390 K

Comparison with PES Comparison with PES (Mo et al. PRL 2004):(Mo et al. PRL 2004):

PM

eg electrons are "localized" and only coherent below ~250K

a1g electrons are "itinerant" and coherent below ~400K"itinerant" and coherent below ~400K

More important for the temperature dependence of the conductivity is, however, that internal structural parameters of V2O3 change with temperature, as we shall see later.

Undo Undo hhybridizationybridization

aa1g1g

eeggππ

PMPM

LDA t2g NMTO Wannier Hamiltonian

2.0

LDALDA

PMPM

a1g-e

gπ c

rys

tal-

fie

ld s

pli

ttin

g =

0.3

eV

U-e

nh

an

ce

me

nt

= 1

.85

eV

~ 3J

LDA+DMFT

U = 4.25 eV, J = 0.7 eV

Crystal-field enhanced Crystal-field enhanced and mass-renormalized and mass-renormalized QP bandsQP bands

PM

eeggππ

aa1g1g

PIPI

= −0.41

1.7

UndoUndo hhybridizationybridization

aa1g1g

eeggππ

390 K

U=4.2 eV, 3.8% Cr, T=580 KU=4.2 eV, 0 % Cr, T=390 K

PM PI

t = -0.72 eV

t = -0.49 eV

t = -0.72 eVt = -0.49 eV

2.0 eV2.0 eV

1.61.61.91.9

1.71.7

V2O3

T=300K(V0.96Cr0.04)2 O3

LDALDA

LDALDA

LDALDA

LDALDA

undo undo aa1g1g--eeggππ

undo undo aa1g1g--eeggππundo undo aa1g1g--eegg

ππ

undo undo aa1g1g--eeggππ

Robinson, Acta Cryst. 1975:

(V(V0.990.99CrCr0.010.01))2 2 OO33 V2O3 at 300K ~ ~ V2O3 at 900K

VV22OO33 33d d ((tt2g2g))22

Hund's-rule coupling

This metal-insulator transition in V2O3 is not,not, like in the case of a single band, e.g. a HTSC:

Hubbard model, LDA+DMFTHubbard model, LDA+DMFTBand 1/2 fullBand 1/2 full

U = 3.0 eV

T=2000KT=2000K

Wannier orbital and LDA Wannier orbital and LDA conduction bandconduction band

U =2.1 eV

T. Saha-DasguptaT. Saha-Dasgupta and OKA 2002 and OKA 2002

caused by disappearance of the quasi-particle peak and driven by the Coulomb repulsion (U),

i.e. it is not really a Mott transition.it is not really a Mott transition.

ConclusionConclusion

In the (t2g)2 system V2O3, described by an LDA tt2g2g

Hubbard model, the metal-insulator transition calculated in the DMFT is caused by quasi-particle bands being

separated by correlation-enhanced correlation-enhanced aa1g1g-e-eggππ crystal-field crystal-field

splitting and lattice distortionsplitting and lattice distortion.

The driving mechanism is multiplet splitting (nJ) rather

than direct Coulomb repulsion (U).

The aa1g1g electrons stay coherentcoherent to higher temperatures

(~450K) than the eeggππ electrons (~250K).